Structural Equation Models

Abstract

More than a decade ago, methods for modeling the structure of relationships among variables with systems of equations began to diffuse among sociologists. Expositions and applications have typically referred to or path analysis, and we use those terms and structural equation interchangeably. We prefer the latter term, since we do not attempt to impose a specific definition of cause. Rather, we take the heuristic view that the meaning of cause resides in the mechanisms thought to be embodied in an equation system. On this matter we are in substantial agree­ ment with the French econometrician Malinvaud (1966): model is the formal representation of the notions that we have about a phenomenon. We think that efforts to impose a narrow definition of cause or effect on the potential application of structural equation are unproductive (Lindsey 1973; Guttman, unpub­ lished manuscript 1976). Sociologists speak of causal models because the term provides a convenient description of what a structural equation system does. In early sociological discussion of these models, Simon (1975) and Blalock (1961, 1962, 1964) employed systems of equations to derive predictions about zero-order and partial correlations. Boudon (1965) noted that coefficients of the system of equations could be estimated and interpreted; in general, such coefficients are not partial correlations. A year earlier, Duncan & Hodge (1964) had estimated coeffi­ cients of a two-equation model of educational and occupational attainment. Indeed, it appears to have been the fruitful application of structural equation to research in social stratification [as exemplified in the work of Blau & Duncan (1967)] rather than an increased statistical sophisticiation among sociologists. that accounts for the rapid diffusion of the use of throughout the discipline. By the late 1960s. a number of expository papers (Duncan 1966. Heise 1968. Land 1968)

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